A022729 Expansion of Product_{m>=1} 1/(1 - m*q^m)^5.

1, 5, 25, 100, 375, 1276, 4155, 12775, 37935, 108460, 301533, 815075, 2153995, 5567685, 14123030, 35183376, 86259665, 208293520, 496100890, 1166243015, 2708878924, 6220640495, 14134118490, 31792023545

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=5 of A297328.

Programs

Magma

n:=50; R:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^5:m in [1..n]])); // G. C. Greubel, Jul 25 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-5, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 25 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^-5)) \\ G. C. Greubel, Jul 25 2018

Formula

G.f.: exp(5*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018